Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent to mat B is Morita equivalent to A.
@article{bwmeta1.element.bwnjournal-article-cmv83i2p295bwm,
author = {Thomas Br\"ustle and Lutz Hille},
title = {Matrices over upper triangular bimodules and $\Delta$-filtered modules over quasi-hereditary algebras},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {295-303},
zbl = {0978.16009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p295bwm}
}
Brüstle, Thomas; Hille, Lutz. Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras. Colloquium Mathematicae, Tome 84/85 (2000) pp. 295-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p295bwm/
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